Question: Solve for $x$ and $y$ using elimination. ${x-4y = 6}$ ${-x-5y = -15}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-9y = -9$ $\dfrac{-9y}{{-9}} = \dfrac{-9}{{-9}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x-4y = 6}\thinspace$ to find $x$ ${x - 4}{(1)}{= 6}$ $x-4 = 6$ $x-4{+4} = 6{+4}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {-x-5y = -15}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(1)}{= -15}$ ${x = 10}$